# Generative Adversarial Nets for Robust Scatter Estimation: A Proper Scoring Rule Perspective

arXiv: https://arxiv.org/abs/1903.01944 · HTML: https://mlsanity.com/paper/1903.01944/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2019.

## Built on by (most cited first, 8 of 8)

- [Adversarial Neuron Pruning Purifies Backdoored Deep Models](https://mlsanity.com/paper/2110.14430/) (2021)
- [Byzantine-Robust Federated Learning with Optimal Statistical Rates and Privacy Guarantees](https://mlsanity.com/paper/2205.11765/) (2022)
- [One-shot Neural Backdoor Erasing via Adversarial Weight Masking](https://mlsanity.com/paper/2207.04497/) (2022)
- [Proper scoring rules for estimation and forecast evaluation](https://mlsanity.com/paper/2504.01781/) (2025)
- [Robust W-GAN-Based Estimation Under Wasserstein Contamination](https://mlsanity.com/paper/2101.07969/) (2021)
- [Robust Estimation for Nonparametric Families via Generative Adversarial Networks](https://mlsanity.com/paper/2202.01269/) (2022)
- [Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances](https://mlsanity.com/paper/2410.20760/) (2024)
- [Hellinger loss function for Generative Adversarial Networks](https://mlsanity.com/paper/2512.12267/) (2025)

## Abstract (arXiv)

Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we introduce a general learning via classification framework based on the notion of proper scoring rules. This framework allows us to understand both matrix depth function and various GANs through the lens of variational approximations of f-divergences induced by proper scoring rules. We then propose a new class of robust scatter estimators in this framework by carefully constructing discriminators with appropriate neural network structures. These estimators are proved to achieve the minimax rate of scatter estimation under Huber's contamination model. Our numerical results demonstrate its good performance under various settings against competitors in the literature.